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Proof step 9 from proof and-size-one (previous step)

bits.first, # bits ≤ # bits1, ∀ bits2, bits1, bits0. # bits2 < # bits → # bits2 ≤ # bits1 ∧ bits2.first → bits2 = [] ∨ bitsand(bits2, bits0 + bits1) = bits0 + bitsand(bits2, bits1) ⊦ bits1 = [], bitsand(bits, bits0 + bits1) = bits0 + bitsand(bits, bits1), bits = [], # bits0 + # bits1 ≠ 1 ∧ bits ≠ true '

User applied rule cut formula

And obtained the following new goals

Proof step 10:
bits = true ', bits.first, # bits ≤ # bits1, ∀ bits2, bits1, bits0. # bits2 < # bits → # bits2 ≤ # bits1 ∧ bits2.first → bits2 = [] ∨ bitsand(bits2, bits0 + bits1) = bits0 + bitsand(bits2, bits1) ⊦ bits1 = [], bitsand(bits, bits0 + bits1) = bits0 + bitsand(bits, bits1), bits = [], # bits0 + # bits1 ≠ 1 ∧ bits ≠ true '

Rule argument

fma: bits = true '

Additional information

Used simplifier rules: ⊦ # bits + # bits0 = 1 ∧ bits ≠ [] → # bits = 1 ∧ bits0 = []; (forward)% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ # bits = 1 ↔ bits = bits.first + [];% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # [] = 0;% ⊦ 0 + m = m;% ⊦ [] + bits = bits; Used formulas: bits = true '